선형대수응용_HW_W12

566 days 전, jongha4886 작성

x1 = vector([1,-2,-1,-3,2,3,0]) x2 = vector([3,-1,1,2,0,-3,-2]) x3 = vector([-4,-2,1,-1,2,-3,0]) x4 = vector([1,2,0,-2,3,-1,-3]) x5 = vector([2,-1,0,3,-2,1,-3]) x6 = vector([1,0,2,1,-1,2,3]) x7 = vector([-1,0,1,2,2,3,0]) A = matrix([x1,x2,x3,x4,x5,x6,x7]) if A.det() != 0: print "A의 모든 행벡터는 일차 독립이며 R^7을 생성합니다." print "따라서 주어진 벡터는 R^7의 기저입니다." B = A.gram_schmidt()[0] B = matrix([B.row(i) / B.row(i).norm() for i in range(0,7)]) if (B*B.transpose() == identity_matrix(7)) & (B.transpose()*B == identity_matrix(7)): print "다음 B의 행벡터들이 R^7의 정규직교기저입니다." print print B 
       
A의 모든 행벡터는 일차 독립이며 R^7을 생성합니다.
따라서 주어진 벡터는 R^7의 기저입니다.
다음 B의 행벡터들이 R^7의 정규직교기저입니다.

[                          1/14*sqrt(7)                          
-1/7*sqrt(7)                          -1/14*sqrt(7)                     
-3/14*sqrt(7)                            1/7*sqrt(7)                    
3/14*sqrt(7)                                      0]
[                   95/1326*sqrt(663/7)                   
-25/663*sqrt(663/7)                       1/78*sqrt(663/7)              
23/1326*sqrt(663/7)                     11/663*sqrt(663/7)              
-1/26*sqrt(663/7)                    -28/663*sqrt(663/7)]
[           -2279/22709*sqrt(22709/663)           
-1627/22709*sqrt(22709/663)              646/22709*sqrt(22709/663)      
-803/22709*sqrt(22709/663)             1538/22709*sqrt(22709/663)       
-1938/22709*sqrt(22709/663)             -178/22709*sqrt(22709/663)]
[        1508/524621*sqrt(524621/22709)       
77215/524621*sqrt(524621/22709)        -3078/524621*sqrt(524621/22709)  
-33577/524621*sqrt(524621/22709)        44769/524621*sqrt(524621/22709) 
-13475/524621*sqrt(524621/22709)       -51249/524621*sqrt(524621/22709)]
[  -317732/1462919*sqrt(1462919/524621)  
-344115/2925838*sqrt(1462919/524621)   
-45865/1462919*sqrt(1462919/524621)   
529915/2925838*sqrt(1462919/524621)  
-145399/1462919*sqrt(1462919/524621)   
675615/2925838*sqrt(1462919/524621) 
-1310511/2925838*sqrt(1462919/524621)]
[   16381/1273669*sqrt(2547338/1462919) 
604911/10189352*sqrt(2547338/1462919)  
846679/1273669*sqrt(2547338/1462919)
1353693/10189352*sqrt(2547338/1462919) 
1028445/5094676*sqrt(2547338/1462919)
2599835/10189352*sqrt(2547338/1462919) 
734773/10189352*sqrt(2547338/1462919)]
[                   -54*sqrt(1/2547338)                 
247/4*sqrt(1/2547338)                   -614*sqrt(1/2547338)            
3989/4*sqrt(1/2547338)                 2037/2*sqrt(1/2547338)           
691/4*sqrt(1/2547338)                 1277/4*sqrt(1/2547338)]
A의 모든 행벡터는 일차 독립이며 R^7을 생성합니다.
따라서 주어진 벡터는 R^7의 기저입니다.
다음 B의 행벡터들이 R^7의 정규직교기저입니다.

[                          1/14*sqrt(7)                           -1/7*sqrt(7)                          -1/14*sqrt(7)                          -3/14*sqrt(7)                            1/7*sqrt(7)                           3/14*sqrt(7)                                      0]
[                   95/1326*sqrt(663/7)                    -25/663*sqrt(663/7)                       1/78*sqrt(663/7)                    23/1326*sqrt(663/7)                     11/663*sqrt(663/7)                      -1/26*sqrt(663/7)                    -28/663*sqrt(663/7)]
[           -2279/22709*sqrt(22709/663)            -1627/22709*sqrt(22709/663)              646/22709*sqrt(22709/663)             -803/22709*sqrt(22709/663)             1538/22709*sqrt(22709/663)            -1938/22709*sqrt(22709/663)             -178/22709*sqrt(22709/663)]
[        1508/524621*sqrt(524621/22709)        77215/524621*sqrt(524621/22709)        -3078/524621*sqrt(524621/22709)       -33577/524621*sqrt(524621/22709)        44769/524621*sqrt(524621/22709)       -13475/524621*sqrt(524621/22709)       -51249/524621*sqrt(524621/22709)]
[  -317732/1462919*sqrt(1462919/524621)   -344115/2925838*sqrt(1462919/524621)    -45865/1462919*sqrt(1462919/524621)    529915/2925838*sqrt(1462919/524621)   -145399/1462919*sqrt(1462919/524621)    675615/2925838*sqrt(1462919/524621)  -1310511/2925838*sqrt(1462919/524621)]
[   16381/1273669*sqrt(2547338/1462919)  604911/10189352*sqrt(2547338/1462919)   846679/1273669*sqrt(2547338/1462919) 1353693/10189352*sqrt(2547338/1462919)  1028445/5094676*sqrt(2547338/1462919) 2599835/10189352*sqrt(2547338/1462919)  734773/10189352*sqrt(2547338/1462919)]
[                   -54*sqrt(1/2547338)                  247/4*sqrt(1/2547338)                   -614*sqrt(1/2547338)                 3989/4*sqrt(1/2547338)                 2037/2*sqrt(1/2547338)                  691/4*sqrt(1/2547338)                 1277/4*sqrt(1/2547338)]